The Thermomechanics of Nonlinear Irreversible Behaviours: An Introduction

FOREWORD v
1. I N T R O D U C T I O N : A post-Duhemian thermodynamics 1
2. THERMOSTATICS A N D T H E R M O D Y N A M I C S
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2.1. Thermodynamic Systems
2.2. Thermodynamic States
2.3. Thermostatics (Born-Caratheodory)
A. Axioms of Thermostatics
B. Scaling of Temperature, Carnot's Theorem
C. Thermodynamic Potentials
D. The Evolution of Real Systems; Continua 17
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3. VARIOUS T H E R M O D Y N A M I C S
3.1. Preliminary Remarks
3.2. Theory of Irreversible Processes (T.I.P.)
A. Axiom of Local State
B. Application to Deformable Material Continua
C. The Compressible Newtonian Fluid
D. The Linear Viscoelastic Solid
E. Finite-Strain Behavior of a Solid
F. Rubber-Like Materials
G. Anisotropic Elastic Materials
H. Onsager-Casimir Symmetry Relations
I. Dissipation Potential 47
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ixContents
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3.3. Rational Thermodynamics
A. General Features
B. Thermoelastic Materials
C. Comparison with T.I.P.
D. Further Improvements
3.4. Extended Thermodynamics
3.5. Thermodynamics with Internal Variables
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4. T H E R M O D Y N A M I C S W I T H I N T E R N A L VARIABLES
4.1. Nature and Choice of Internal Variables
4.2. Internal Variables and Functional Constitutive Equations
4.3. Non-Equilibrium and Equilibrium States
4.4. Accompanying Processes and States
A. Verbal Statement of the L.A.S.
B. Formal Statement of the L.A.S.
4.5. Applying T.I.P. to T.I.V.
4.6. Potentials of Dissipation
4.7. Internal Variables and Microstructure
A. Highly Heterogeneous Bodies
B. Internal Variables or Internal Degrees of Freedom?
4.8. Internal Variables and Phase Transitions
4.9. Comparison with Extended Thermodynamics 77
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5. APPLICATIONS: G E N E R A L F R A M E W O R K
5.1. Summary
5.2. Convexity of the Energy
5.3. General Properties of Dissipation Potentials
5.4. Convex Pseudo-Potential of Dissipation
5.5. Nonconvex Dissipation Potential
5.6. Reminder of Basic Equations
A. The Case Solids
B. The Case of Fluids 107
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6. VISCOSITY I N COMPLEX FLUIDS
6.1. Introductory Remarks
6.2. The Notion of Simple (Non-Newtonian) Fluid
6.3. Statistical Theory of Polymeric Fluids
A. Molecular Models 129
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133Contents
6.4.
6.5.
6.6.
6.7.
6.8.
6.9.
B. Evolution Equation for the Conformation
C. Stress Tensor
Thermodynamics with Internal Variables
A. General View
B. The Internal Variable is an Anelastic Strain
C. The Internal Variable is a Conformation
D. The Internal Variable is a Vector
E. The Internal Variable is a Scalar
F. Forced Thermodynamic Systems
Diffusion and Migration
Vorticity and Conformation
Liquid Crystals
Structurally Complex Flows
Conclusions
XI
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7. VISCOPLASTICITY A N D PLASTICITY
7.1. Introductory Remarks
7.2. Viscoelasticity of Solids
7.3. Plasticity and Viscoplasticity in Small Strains
7.4. Plasticity and Viscoplasticity in Finite Strains
7.5. Damage, Cyclic Plasticity and Creep
7.6. Relationship with Microscopic Theory
7.7. Remarks on Elastoplastic Composites
7.8. Remark on the Heat Equation 167
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8. T H E R M O D Y N A M I C S OF F R A C T U R E
8.1. Preliminary Remark
8.2. Energy Aspects of Brittle Fracture
(no thermal fields)
8.3. On Account of Thermal Fields
8.4. Material Forces in Fracture
A. General Features
B. Evaluation of Elementary Dissipation
C. Global Balances of Momentum
D. Energy Argument
8.5. The Use of Generalized Functions in the Energy Equation
8.6. Remark on Cases Exhibiting Local Dissipation 197
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9. N O N - E Q U I L I B R I U M T H E R M O D Y N A M I C S OF
ELECTROMAGNETIC MATERIALS
9.1. General Remarks
9.2. Reminder on Electromagnetism
9.3. Thermomechanics of Electromagnetic Materials
9.4. Classical Irreversible Processes:
Conduction and Relaxation
A. Rigid Bodies
B. Fluids
C. Deformable Solids
9.5. Thermodynamics with Internal Variables
A. Magnetic Solids in Small Strains
B. Electrically Polarized Solids in
Finite Strains
9.6. Dielectric Relaxation in Ceramics
A. Delayed-Wave Analysis
B. Instantaneous Wave
9.7. Electro- and Magnetomechanical Hysteresis
A. Electric Bodies
B. Magnetic Bodies
C. Relation to Microscopic Descriptions
9.8. Elastic Superconductors
9.9. Solutions of Polyelectrolytes
A. Thermodynamical Modeling
B. Field Equations
C. Dissipative Processes
D. Mechano-Chemical Effect
E. Electrically Induced Conformational
Phase Transition
F. Kerr Effect
9.10. Ferroelectrics and Ferromagnets
A. Deformable Ferromagnets
B. Elastic Ferroelectrics
9.11. Solutions of Magnetic Fluids
9.12. Electroelastic and Magnetoelastic Fracture
9.13. Concluding Remarks
Contents
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292Contents
10. WAVES A N D REACTION-DIFFUSION
SYSTEMS (RDS)
10.1. Preliminary Remarks
10.2. Simple RDS'
10.3. Models of Nerve-Pulse Dynamics: A Good Physical
Example of Internal-Variable Theory
A. Nerve-Pulse Transmission
B. Thermodynamics of Nerve-Pulse Dynamics:
FHN Model
C. Hodgkin-Huxley Model
D. More Complex Relaxation Equations
E. Some Conclusive Remarks
10.4. Coherent Phase-Transition Fronts: Another Example
of Thermodynamics of Material Forces
A. The General Problem
B. Quasi-Static Progress of a Coherent
Phase-Transition Front
C. Heat-Conducting Case
X11I
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BIBLIOGRAPHY 325
SUBJECT INDEX 359